Accurate time propagation for the Schrödinger equation with an explicitly time-dependent Hamiltonian

Journal of Chemical Physics

Volumn 128, Issue 18, 2008, Pages

  Kormann, Katharina ^a   Holmgren, Sverker ^a   Karlsson, Hans O ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC COMMUTATORS; HAMILTONIANS; MATHEMATICAL MODELS; NUMERICAL METHODS;

MAGNUS-LANCZOS APPROACH; PUMP-PROBE EXPERIMENTS; SPLIT-OPERATOR METHOD; TIME-DEPENDENT HAMILTONIANS;

SCHRODINGER EQUATION;

EID: 43949108557     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2916581     Document Type: Article

References (35)

1. A. H. Zewail, Femtochemistry (World Scientific, Singapore, 1994).
2. C. Leforestier, R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, J. Comput. Phys. 94, 59 (1991).
3. C. Lubich in Quantum Simulation of Complex Many-Body Systems: From Theory to Algorithms, edited by, J. Grotendorst, D. Marx, and, A. Muramatsu, (John von Neumann Institute for Computing, Jülich, 2002), p. 459.
4. D. J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective (University Science Books, Sausalito, 2007).
5. J. M. Sanz-Serna and A. Portillo, J. Chem. Phys. 104, 2349 (1996).
6. P. Schwendner, F. Seyl, and R. Schinke, Chem. Phys. 217, 233 (1997).
7. W. Magnus, Commun. Pure Appl. Math. 7, 649 (1954).
8. A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna, Acta Numerica 9, 215 (2000).
9. I. I. Rabi, Phys. Rev. 51, 652 (1937).
10. B. C. Hall, Lie Groups, Lie Algebras, and Representations (Springer, New York, 2003).
11. U. Peskin, R. Kosloff, and N. Moiseyev, J. Chem. Phys. 100, 8849 (1994).
12. S. K. Gray and J. M. Verosky, J. Chem. Phys. 100, 5011 (1994).
13. R. J. Littlejohn, Phys. Rep. 138, 193 (1986).
14. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer-Verlag, Berlin, 2004).
15. S. Blanes and P. C. Moan, J. Comput. Appl. Math. 142, 313 (2002).
16. S. Blanes, F. Casas, and A. Murua, J. Chem. Phys. 124, 234105 (2006).
17. S. K. Gray and D. E. Manolopoulos, J. Chem. Phys. 104, 7099 (2006).
18. R. I. McLachlan, SIAM J. Sci. Comput. (USA) 16, 151 (1995).
19. M. D. Feit and J. A. Fleck, J. Chem. Phys. 78, 301 (1983).
20. G. Strang, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 5, 506 (1968).
21. S. Blanes, Appl. Numer. Math. 37, 289 (2001).
22. R. I. McLachlan and G. R. W. Quispel, Acta Numerica 11, 341 (2002).
23. S. Blanes, F. Casas, and A. Murua, Found. Comput. Math., Report No. NA2006_08, 2006.
24. S. Blanes and P. C. Moan, Phys. Lett. A 295, 35 (2000).
25. T. J. Park and J. C. Light, J. Chem. Phys. 85, 5870 (1986).
26. J. W. Demmel, Applied Numerical Linear Algebra (SIAM, Philadelphia, 1997).
27. M. Hochbruck, C. Lubich, and H. Selhofer, SIAM J. Sci. Comput. (USA) 19, 1552 (1998).
28. H. Tal-Ezer, R. Kosloff, and C. Cerjan, J. Comput. Phys. 100, 179 (1992).
29. S. Blanes, F. Casas, and J. Ros, BIT Numerical Mathematics 40, 434 (2000).
30. N. Gador, B. Zhang, H. O. Karlsson, and T. Hansson, Phys. Rev. A 70, 033418 (2004).
31. S. Blanes and P. C. Moan, Appl. Numer. Math. 56, 1519 (2006).
32. P. Pechukas and J. C. Light, J. Chem. Phys. 44, 3897 (1966).
33. M. Hochbruck and C. Lubich, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 41, 945 (2003).
34. S. J. Park, S. W. Suh, Y. S. Lee, and G.-H. Jeung, J. Mol. Spectrosc. 207, 129 (2001).
35. J. M. Sanz-Serna and M. P. Calvo, Numerical Hamiltonian Problems (Chapman and Hall, London, 1994).